The invention disclosed and claimed herein generally pertains to a method and apparatus for improving accuracy in computed tomography (CT) cone-beam imaging. More particularly, the invention pertains to such method and apparatus wherein x-ray projection data is converted to Radon planar integral data. Even more particularly, the invention pertains to reducing distortion in computing the Radon derivative proximate to the edge or boundary region of a projected image.
One of the most important techniues currently used in constructing a CT image of an object is based on the Radon transform. This technique is of particular importance in three-dimensional (3D) CT imaging. According to such technique, a cone-beam x-ray source irradiates the object to project an image of the object, in the form of cone-beam x-ray data, on to a detector plane. A two-step process is then performed, wherein the cone-beam data is converted into a set of Radon data, or planar integrals defined in Radon space, and an inverse Radon transform is performed using the planar integrals to construct the image. It is known that this process is most usefully carried out by computing the radial derivative (Radon derivative) for each planar integral in the set, from which the values of respective planar integrals can be readily determined.
Commonly assigned U.S. Pat. No. 5,257,183, issued Oct. 26, 1993 to Kwok C. Tam, the inventor named herein, discloses a very efficient technique for computing the Radon derivatives for use in the above process. Such patent teaches a method wherein a given planar integral is taken in a plane Q, the plane Q being extended to intersect the normalized detector plane along a line L. A line L' is then rotated in the detector plane from the line L, so as to lie at a small angle .alpha. with the line L. The cone-beam data lying along the lines L and L' is integrated to generate respective corresponding weighted line integrals J and J'. The Radon derivative for the given planar integral is then calculated from the difference between the weighted line integrals, divided by an angle .beta., which is geometrically related to the small angle of rotation .alpha.. More particularly, .beta. is the angle between the plane Q and the plane Q', which intersects the detector plane along line L', and is rotated from plane Q about an axis which intersects the line L at a point C. Hereinafter, the point C is referred to as the center of rotation. The relationship between angle .alpha. and angle .beta. is clearly and completely set forth in U.S. Pat. No. 5,257,183, referred to above. Thus, if R' is the Radon derivative for a given planar integral, R'=(J-J')/.beta.
While the Radon derivative method described above works quite well, there is a concern with possible inaccuracy with respect to regions close to the edge of the projected image. Since the method requires taking the difference between weighted line integrals along two spaced apart lines on the detector plane, a discontinuity could be encountered between the lines. For example, the line L could intersect the projected image close to the edge thereof, but the line L' would be rotated to a position such that it did not intersect the image at all.